Someone who is purposefully posting on a forum/messageboard/site sith the sole aim to irritate the regular members.

Contrary to popular belief there is much more to internet trolling than posting "OMG UR ALL SO GHEYYYY!!!1" "OMFG TRIVIUM SUX ASS U FAGS LOL" and the like. People who post such things will usually be one-post wonders and get banned, however the more experienced troll will attempt to cause some sort of havoc under the admins radar.

Common examples of trolling:
The long-term troll:
These guys don't mind waiting around for the fun to begin. They may pretend to be an average n00b, and give themselves the stereotyical interest(s) of the average member of said forum, then once having a few posts they will gradually try to spread dissent. This type may even pretend to be pally to the admin and get their msn (and try to crack their account password of course) whilst causing general disruption. May act under other proxies and slate these fake trolls on msn to the aforementioned gullible admin. These people, to be frank, usually have no life and love bringing message boards to their knees by putting considerable time into their carnage. If they crack the admins password the board is doomed.

The sophisticated troll:
This type will usually have some sort of distaste for whatever the said message board is discussing and try to cause annoyance as opposed to destructiveness. They will parody the members and see how much they can get over their heads. Subtle pisstaking being their route. They'll usually get banned in the end but will annoy an entire community using this drawn out approach.

The faker troll:
A clever troll, the main aim of the game is to, ironically, act really REALLY stupid, this trolls aim is to argue with members incoherantly, usually using text speak. This is a ploy, the troll only needs to spend 10 seconds writing the babble when the member wastes 10 minutes writing a much more wordy reply. The troll will reply with a stupid rebuff making the member post as many long replies as possible. Using the members weight against them and wasting their forum time... If they are good then their act will be believable and they probably won't get banned unless the admin is strict on txt tlk.

The rank and file spammer:
These are the first to pop into peoples minds, they are similar to the examples stated in the first paragraph. No previous experience necessary, this lot will swarm in, again, usually under proxies to maximise the destructiveness, and spam the place to hell. Only causes mild irritation if not in large numbers.

Join any popular forum for a year and I guarantee you'll see all of these.

1) A fantasy creature with no single definition. Usually large, ugly and nasty...except when it's small, cute, and friendly. Often lives under bridges.

2) An ugly little plastic doll with big hair.

3) One of the five Horde races in World of Warcraft. Tall, leggy, and blue, with three-fingered hands and two-toed feet; also has tusks and a Caribbean accent.

4) (verb) To go fishing.

5) (verb) To act as an example of the Greater Internet Fuckwad Theory; derived from definition 4, on the theory that the person is "fishing" for attention. This can also be a noun, meaning someone who does just that.

A troll in the sense of an internet troll has many different meanings. Not all trolls go to a message board and spam it with flames, racism, and Goatse before getting banned 5 minutes later. Trolling is a hobby in the same vein as prank phone calls, and the true objective of trolling is to be clever and creative in getting a reaction out of the troll victims.
Skilled trolls especially like trolling large-scale websites such as MySpace or LiveJournal where it is harder to get banned. Trolling a site such as GameFAQs is more difficult, as the TOS is very strict and the moderators are harder on trolls.

Somebody who likes to buy fruit at the local fruit stand. Trolls typically like dragon fruit and pomegranates. Trolls can be identified by the fact that they wear nothing but a green paper plate over their genitals and a red plastic cup on their head. Trolls also have the belief that giraffes do not exist. Do not try to reason with them that they do for they will tear your scapula out with a rusty spoon.

Do you know where I can get some really cheap pomegranates?" "I hear the local troll is selling them way cheaper than the fruit stand.

While hated by most, these people are typically non-social for reasons beyond their control, and manage to get that one glimpse at society by eliciting responses from forum-goers who, nine times out of ten, think they know everything and that anything that goes against the norm is bad. There are of course the assholes who do it just for fun, but a lot of these people are suffering: people with manic (or often just plain old) depression, people with real issues in real life, or people who's real life isn't as cupcakes and unicorns as people on the internet assume.

I say this because I know people in real life who many would consider trolls, and they "troll" on forums because they receive no attention from their family and very little from anyone else. They are saints for putting up with it in real life, but it'd be unhealthy to pent up all their frustration. So what do they do? They speak out on the internet, often in obnoxious and annoying matters. The very fact that people respond to what they say is important to them, just because they get satisfaction in knowing that some people somewhere acknowledge their existence, and perhaps more importantly their opinion. Believe me, most trolls you see aren't "a poor excuse of a human being". Their lives in real life is worse than many could imagine. Everyone needs to vent sometimes.

Troll: WOW U FUCKS NARUTO IS FOR HOMOS ONLY.

Forum-goers: U poor excuse for a human being you need to die

Troll (in real life): Man, I don't really like Naruto. But no one knows that. No one in my life give a flying fuck about anything I say or do.